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The quantum speed limit (QSL) is a theoretical lower bound of the time required for a
quantum system to evolve from an arbitrary initial state to its orthogonal counterpart. This figure
can be used to characterize the dynamics of open quantum systems, including non-Markovian maps.
In this paper, we investigate the QSL time for a model that consists of a single qubit moving inside
a leaky cavity. Notably, we show that for both weak and strong coupling regimes, the QSL time
increases while we boost the velocity of the qubit inside the leaky cavity. Moreover, it is observed that
by increasing the qubit velocity, the speed of the evolution tends to a constant value, and the system
becomes more stable. The results provide a better understanding of the dynamics of atom-photon
couplings and can be used to enhance the controllability of quantum systems.
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